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Abstract:
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Although modes often have different measurement properties, standard practice is to collapse mixed-mode together, neglecting the potential impacts of mode effects. This study proposes a “Testimator” approach, a Bayesian approach, and a model averaging approach. In the “Testimator” approach, we test whether the means and variances of mixed-mode samples are the same. If the null hypothesis fails to reject, we take the average of the estimates; otherwise, we take the estimate in the preferred direction (assumed known). In the Bayesian approach, we use estimated effect size and ratio of variances to determine cutoffs of mode effects and use the probability of the two quantities falling into different cutoff areas as weights to combine estimates. In the last approach, we combine estimates of four models (which assume same or different means and same or different variances across modes) using marginal posteriors as weights. Compared to existing methods, our proposed methods incorporate testing procedures into inference, thus providing robust inference. We evaluate the approaches in a simulation study and find they reduce bias in some scenarios.
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